A photometric function of planetary surfaces for gourmets

Abstract

A new photometric model with small number of parameters is presented. The model is based on an assumption that there exist such surfaces for which spatial brightness variations caused by small topography undulations can be reproduced exactly by corresponding spatial variations of albedo. This indistinguishability results in a differential equation suggesting a new photometric function that generalizes, in particular, the Akimov disk-function. Our model provides excellent fits in a wide phase-angle range for integral observations of asteroids of different albedos. We also carried out fitting to integral observations of the Moon and Mercury, confirming difficulties in describing Mercury's phase function at large phase angles, which were also found for the Hapke model. Comparisons of global latitude and longitude trends with our model calculations have shown good coincidence for the Moon. To retrieve the lunar trends, we use the phase-ratio technique, applying it to our telescope observations. Mapping the model parameters using LROC WAC data were carried out for a region comprising the Reiner Gamma formation. This mapping allows us to calculate phase-ratio images of the region, showing at large phase angles systematically steeper phase curves of young craters and smaller steepness for the very Reiner Gamma formation.